Unable to remove unwanted edges after fill
There is no way to clean all edges in your object. Since blender cant handle holes inside n-gon by one face. You can make nicer topology by manual reconecting some of the edges (or try to search for Beautiful Fill function), but you will need always at least two faces (two edges connected to a hole).



In some cases would be better simply select object and Convert to Curve type 2D. No more additional edges, just outlines.